Chapter 11 Keys, Couplings and Seals RJM 3/16/04
Chapter 11 - Keys, Couplings and Seals
•How attach power transmission components to shaft to prevent rotation and axial motion?
Torque resistance: keys, splines, pins, weld, press fit, etc..
Axial positioning: retaining rings, locking collars, shoulders machined into shaft, etc….
•What is the purpose of rigid and flexible couplings in a power transmission system?
•Specify seals for shafts and other types of machine elements.
11.1 Chapter Objectives:
Chapter 11 Keys, Couplings and Seals RJM 3/16/04
11.2 Keys
Most common for shafts up to 6.5” is the square and rectangular keys:
1. Cost effective means of locking the
2. Can replace damaged component
3. Ease of installation
4. Can use key as “fuse” – fails in shear at some predetermined torque to avoid damaging drive train.
Figure 11.1
Advantages:
Chapter 11 Keys, Couplings and Seals RJM 3/16/04
Square and rectangular keys:
Step 1 – Determine key size based on shaft diameter
Step 2 – Calculate required length, L, based on torque (11.4)
Chapter 11 Keys, Couplings and Seals RJM 3/16/04
SHAFT BORE
Step 3 – Specify appropriate shaft and bore dimensions for keyseat:
See Figure 11.2
Note, should also specify fillet radii and key chamfers – see Table 11-2
For 5/16” key
Chapter 11 Keys, Couplings and Seals RJM 3/16/04
Other types of keys:
a. Tapered key – can install after hub (gear) is installed over shaft.
b. Gib head key – ease of extraction
c. Pin keys – low stress concentration
d. Woodruff key – light loading offers ease of assembly
Chapter 11 Keys, Couplings and Seals RJM 3/16/04
11.4 Design of Keys – stress analysis to determine required length:
=
No load
Torque being transmitted
T = F/(D/2) or F = T/(D/2) this is the force the key must react!!!
Chapter 11 Keys, Couplings and Seals RJM 3/16/04
Shear stress
Bearing stress
Required Length based on Shear Stress:
NSywhereDWTL d
d
/5.02
Required Length based on Bearing Stress:
NSywhereDHTL d
d
/4
Typical parameters for keys:
N = 3, material 1020 CD (Sy = 21,000 psi)
Chapter 11 Keys, Couplings and Seals RJM 3/16/04
Example: Specify the complete key geometry and material for an application requiring a gear (AISI OQT 1000) with a 4” hub to be mounted to a 3.6” diameter shaft (AISI 1040 CD). The torque delivered through the system is 21,000 lb-in. Assume the key material is 1020 CD (Sy = 21,000 psi) and N = 3.
Solution (note since key is weakest material, focus analysis on key!):
See handout
Chapter 11 Keys, Couplings and Seals RJM 3/16/04
11.4 Splines
Advantages:
•Can carry higher torque for given diameter (vs keys) or
•Lower stress on attachment (gear)
•Better fit, less vibration (spline integral to shaft so no vibrating key)
•May allow axial motion while reacting torque
Disadvantage:
•Cost
•Impractical to use as fuse
Chapter 11 Keys, Couplings and Seals RJM 3/16/04
Splines
“Axial keys” machined into a shaft
Transmit torque from shaft to another machine element
Chapter 11 Keys, Couplings and Seals RJM 3/16/04
Advantages• Uniform transfer of torque• Lower loading on elements• No relative motion between “key” and shaft• Axial motion can be accommodated (can
cause fretting and corrosion)• Mating element can be indexed with a
spline• Generally hardened to resist wear
Chapter 11 Keys, Couplings and Seals RJM 3/16/04
Spline Types• Straight
– SAE– 4, 6, 10 or 16 splines
• Involute – Pressure angles of 30, 37.5, or 45 deg.– Tend to center shafts for better
concentricity
Chapter 11 Keys, Couplings and Seals RJM 3/16/04
SAE Spline Sizes
A: Permanent Fit
B: Slide without Load
C: Slide under Load
Pg 504
Chapter 11 Keys, Couplings and Seals RJM 3/16/04
Two types of splines:
Straight Sided Involute:
Chapter 11 Keys, Couplings and Seals RJM 3/16/04
Use this for spline design – SAE formulas based on 1,000 psi bearing stress allowable!!
Use this to get diameter. Then table 11.4 to get W, h, d
Chapter 11 Keys, Couplings and Seals RJM 3/16/04
Torque Capacity
• Torque capacity is based on 1000 psi bearing stress on the sides of the splines
T = 1000*N*R*hN = number of splinesR = mean radius of the splinesh = depth of the splines
Chapter 11 Keys, Couplings and Seals RJM 3/16/04
Torque Capacity Cont’d
)dD(21h
4dD
2dD
21R
8
dDN10002
dD4
dDN1000T22
Substituting R and h into torque equation:
Chapter 11 Keys, Couplings and Seals RJM 3/16/04
Torque Capacity Cont’d• Further refinement can be done by
substituting appropriate values for N and d.
• For 16 spline version, with C fit, N = 16 and d = .810D
2
22
D688T
8)D810(.D)16(1000T
688/TD
Torque in IN-LBS/INCH of spline
Required D for given Torque
Chapter 11 Keys, Couplings and Seals RJM 3/16/04
Torque Capacity for Straight Splines
Pg 505
Chapter 11 Keys, Couplings and Seals RJM 3/16/04
Torque Capacity for Straight Splines
Chapter 11 Keys, Couplings and Seals RJM 3/16/04
Example: A chain sprocket delivers 4076 in-lbs of torque to a shaft having a 2.50 inch diameter. The sprocket has a 3.25 inch hub length. Specify a suitable spline having a B fit.
T = kD2LT = torque capacity in in-lbskD2 = torque capacity per inch
(from Table 11-5)L = length of spline in inches
Chapter 11 Keys, Couplings and Seals RJM 3/16/04
Example Continued
• From Table 11-5, use 6 splines
2017.200)"25.3()"50.2(
lbsin4076LD
Tk 22
Chapter 11 Keys, Couplings and Seals RJM 3/16/04
Torque Capacity for Straight Splines
4076/3.25
2.5
Chapter 11 Keys, Couplings and Seals RJM 3/16/04
Example: Specify straight spline for the previous problem (i.e. Torque = 21,000 lb-in and shaft is 3.6 in diameter.
Chapter 11 Keys, Couplings and Seals RJM 3/16/04
Taper & Screw
Expensive – machining
Good concentricity
Moderate torque capacity
Can use a key too
Chapter 11 Keys, Couplings and Seals RJM 3/16/04
Couplings• Used to connect two shafts together at
their ends to transmit torque from one to the other.
• Two kinds of couplings:– RIGID– FLEXIBLE
Chapter 11 Keys, Couplings and Seals RJM 3/16/04
Rigid Couplings
NO relative motion between the shafts.
Precise alignment of the shafts
Bolts in carry torque in shear. N = # of bolts.
)(NDT8d
dbc
Chapter 11 Keys, Couplings and Seals RJM 3/16/04
Flexible Couplings• Transmit torque smoothly• Permit some axial, radial and angular
misalignment
Chapter 11 Keys, Couplings and Seals RJM 3/16/04
Flexible Couplings
Chapter 11 Keys, Couplings and Seals RJM 3/16/04
Flexible Couplings
Chapter 11 Keys, Couplings and Seals RJM 3/16/04
Lord Corp. Products
Chapter 11 Keys, Couplings and Seals RJM 3/16/04
Flexible Coupling
Chapter 11 Keys, Couplings and Seals RJM 3/16/04
Universal JointsLarge shaft misalignments permissible
Key factors in selection are Torque, Angular Speed and the Operating Angle
Output not uniform wrt input Output IS uniform wrt input
Chapter 11 Keys, Couplings and Seals RJM 3/16/04
Axial Constraint Methods
Retaining ring
Retaining ring
Shoulders
Spacers
Chapter 11 Keys, Couplings and Seals RJM 3/16/04
Retaining Rings
Chapter 11 Keys, Couplings and Seals RJM 3/16/04
Locknuts